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    Numerical Stability Analysis of Linear Incommensurate Fractional Order Systems

    Source: Journal of Computational and Nonlinear Dynamics:;2013:;volume( 008 ):;issue: 004::page 41012
    Author:
    Das, Sambit
    ,
    Chatterjee, Anindya
    DOI: 10.1115/1.4023966
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: We present a method for detecting right half plane (RHP) roots of fractional order polynomials. It is based on a Nyquistlike criterion with a systemdependent contour which includes all RHP roots. We numerically count the number of origin encirclements of the mapped contour to determine the number of RHP roots. The method is implemented in Matlab, and a simple code is given. For validation, we use a Galerkin based strategy, which numerically computes system eigenvalues (Matlab code is given). We discuss how, unlike integer order polynomials, fractional order polynomials can sometimes have exponentially large roots. For computing such roots we suggest using asymptotics, which provide intuition but require human inputs (several examples are given).
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      Numerical Stability Analysis of Linear Incommensurate Fractional Order Systems

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    http://yetl.yabesh.ir/yetl1/handle/yetl/151162
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    contributor authorDas, Sambit
    contributor authorChatterjee, Anindya
    date accessioned2017-05-09T00:57:01Z
    date available2017-05-09T00:57:01Z
    date issued2013
    identifier issn1555-1415
    identifier othercnd_8_4_041012.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/151162
    description abstractWe present a method for detecting right half plane (RHP) roots of fractional order polynomials. It is based on a Nyquistlike criterion with a systemdependent contour which includes all RHP roots. We numerically count the number of origin encirclements of the mapped contour to determine the number of RHP roots. The method is implemented in Matlab, and a simple code is given. For validation, we use a Galerkin based strategy, which numerically computes system eigenvalues (Matlab code is given). We discuss how, unlike integer order polynomials, fractional order polynomials can sometimes have exponentially large roots. For computing such roots we suggest using asymptotics, which provide intuition but require human inputs (several examples are given).
    publisherThe American Society of Mechanical Engineers (ASME)
    titleNumerical Stability Analysis of Linear Incommensurate Fractional Order Systems
    typeJournal Paper
    journal volume8
    journal issue4
    journal titleJournal of Computational and Nonlinear Dynamics
    identifier doi10.1115/1.4023966
    journal fristpage41012
    journal lastpage41012
    identifier eissn1555-1423
    treeJournal of Computational and Nonlinear Dynamics:;2013:;volume( 008 ):;issue: 004
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
    yabeshDSpacePersian